Projective Measurement of a Single Nuclear Spin Qubit by Using Two-Mode Cavity QED

We report the implementation of projective measurement on a single $1/2$ nuclear spin of the ${}^{171}\mathrm{Yb}$ atom by measuring the polarization of cavity-enhanced fluorescence. To obtain cavity-enhanced fluorescence having a nuclear-spin-dependent polarization, we construct a two-mode cavity QED system, in which two cyclic transitions are independently coupled to each of the orthogonally polarized cavity modes, by manipulating the energy level of ${}^{171}\mathrm{Yb}$. This system can associate the nuclear spin degrees of freedom with the polarization of photons, which will facilitate the development of hybrid quantum systems.

Figure 1

(a) Relevant energy-level diagram of ${}^{171}\mathrm{Yb}$. $|\uparrow ⟩$ and $|\downarrow ⟩$ denote the magnetic substates $m_I=\pm 1/2$ in the ground state of ${}^{1}S_0(I=1/2)$. (b) Schematic of the experimental apparatus. MOT: magneto-optical trap, $\lambda /4$ plate: quarter-wave plate, PBS: polarizing beam splitter, SPCM: single-photon-counting module.

Figure 2

(a) Hyperfine spectroscopy on the ${}^{3}D_1$ state of ${}^{171}\mathrm{Yb}$. The fluorescence from the MOT are collected by a photomultiplier while shining the light-shift beam. (b),(c) The cavity-enhanced fluorescence spectrum. The atoms are irradiated (b) without and (c) with the light-shift beam. The frequencies of both the excitation and the lock beam are simultaneously changed.

Figure 3

Scattering diagrams of ${\sigma }_{+}$ and ${\sigma }_{-}$ counts (a) without and (b) with irradiation of the light-shift beam. The squares (circles) correspond to $|\uparrow ⟩$ ($|\downarrow ⟩$).

Figure 4

Fluorescence detection at the level of single atom. (a) Histograms of total counts ($n_{\mathrm{to}}={\sigma }_{+}+{\sigma }_{-}$) in the fluorescence detection (hatched histogram) and in the dark counts (empty histogram). (b) Histograms of difference counts ($n_{\mathrm{di}}={\sigma }_{+}-{\sigma }_{-}$) for the initial spin $|\uparrow ⟩$ (hatched histogram) and $|\downarrow ⟩$ (empty histogram). The inset shows the theoretically calculated SNR as a function of the light-shift beam power. A Gaussian profile with $w_l=50\mu \mathrm{m}$ is assumed. The cross mark is the experimental value.